Constant Coefficients Research Articles

Generalizations of the Jacobi identity to the case of the Lauricella function F D ( N )

ABSTRACT The paper considers the issue of constructing differential relations for the Lauricella hypergeometric function F D ( N ) . The formulas found give explicit expressions for the derivative of the product of the function F D ( N ) and some binomials through the product of other binomials and a combination of adjacent Lauricella functions whose parameters differ by 1 or − 1 . The derived differential relations generalize the Jacobi identity and other differential formulas known in the theory of the Gauss hypergeometric function on the multidimensional case. With special parameter values F D ( N ) , the right-hand side of such Jacobi-type formulas are simplified and have the form of a product of binomials and a polynomial. Such formulas can be used to transform a Cauchy-type integral to the form of the Schwartz–Christoffel integral and have an application to the Riemann–Hilbert problem with piecewise constant coefficients.

Bounded in the mean and stationary solutions of second-order difference equations with operator coefficients

We study the question of the existence of a unique bounded in the mean solution for the second-order difference equation with piecewise constant operator coefficients and of the stationary solution of the corresponding difference equation with constant operator coefficients. The case is considered when the corresponding “algebraic” operator equations have separated roots.

Influence of operational excellence strategy on organisations’ competitiveness among tier III category of Commercial Banks in Kenya

Tier 3 Kenyan commercial banks face significant challenges, including intense competition, financial distress, and declining profits despite consistent loan growth. This study investigates the impact of operational excellence strategies on the competitiveness of these banks using a pragmatic research approach that combines qualitative and quantitative methods. The study is grounded in the dynamic capabilities theory and collected data from 288 respondents across various management roles within the banks through semi-structured questionnaires. The data were analyzed using thematic analysis for qualitative data and SPSS for quantitative data, including descriptive statistics, regression analysis, and ANOVA. The regression model revealed a moderate positive relationship between operational excellence and organizational competitiveness, with a correlation coefficient (R) of 0.685. The coefficient of determination (R Square) was 0.469, indicating that operational excellence accounts for 46.9% of the variability in competitiveness. The coefficient for Operational Excellence is 1.260 (standard error = 0.087, beta = 0.685), with a t-value of 14.493 and a significance level of 0.000. The constant coefficient is -1.565 (standard error = 0.353, t-value = -4.437). This study underscores the importance of strategic investments in operational excellence practices to enhance organizational efficiency and sustainable competitive advantages. However, the study's scope is limited to tier III commercial banks in Kenya, and future research should explore additional factors influencing competitiveness and include a broader sample for improved generalizability.

The New Integral Transform “Bayawa Transform”

In this paper a new integral transform namely Bayawa transform is proposed to solve linear ordinary differential equations with constant coefficients

An Eulerian–Lagrangian method of fundamental solutions for the advection–diffusion equation with time dependent coefficients

This paper investigates the application of the Eulerian–Lagrangian method of fundamental solutions (ELMFS), a truly meshless method that couples the Euler–Lagrange Method (ELM) with the time-dependent method of fundamental solution (MFS). It is applied to solve the transient advection–diffusion equation with transport coefficients exhibiting constant and temporally exponential behaviors. The stability and accuracy of the proposed method were analyzed in terms of condition numbers, location of source points, and error metrics. The stability results for constant coefficients of partial differential equations are presented in a map and compared with well-established stability criteria for explicit in-time mesh methods, such as the Courant–Friedrichs–Lewy and Von Neumann criteria. These comparisons demonstrate that ELMFS has larger stable regions.

Polymer Nanocomposite Based on Pyrolyzed Polyacrylonitrile Doped with Carbon Nanotubes: Synthesis, Properties, and Mechanism of Formation

The paper investigates the possibility of fabricating a carbon nanotubes (CNT)-modified nanocomposite based on pyrolyzed polyacrylonitrile (PPAN). The layered structure of PPAN ensures the attachment of nanotubes (NT) to the polymer matrix, forming enhanced PPAN/CNT nanocomposites. We synthesized a PPAN/CNT polymer nanocomposite and investigated its mechanical, conductive, and electronic properties. Using the quantum chemical method density functional theory (DFT), we studied an interaction mechanism between PPAN and single-walled carbon nanotubes. We described the structural features and electron energy structure of the obtained systems. We found that the attachment of a CNT to the PPAN matrix increases tensile strength, electrical conductivity, and thermal stability in the complex. The obtained materials were exposed to electromagnetic radiation and the dielectric constant, reflection, transmission, and absorption coefficients were measured. The study demonstrates the possibility of using carbon nanotubes for reinforcing polyacrylonitrile polymer matrix, which can result in the development of an enhanced class of materials possessing the properties of both polymers and CNTs.

Radially transverse isotropic inclusions in isotropic elastic media: Local fields, neutral inclusions, effective elastic properties

Radially transverse isotropic inclusions in homogeneous isotropic elastic host media are considered. Mellin transform method is used for solution of the volume integral equation of the problem for an isolated inclusion subjected to a constant external stress (strain) field. The tensor structure of the solution is revealed with precision to three scalar functions of the radial coordinate, and the system of ordinary differential equations for these functions is derived. For multilayered radially transverse isotropic inclusions with constant elastic coefficients inside layers, explicit solution of these equations is obtained. An efficient numerical algorithm of solution for inclusions with an arbitrary number of the layers is proposed. Neutral inclusions that do not disturb homogeneous external fields applied to the medium are considered. It is shown that an inclusion with an isotropic core and radially transverse isotropic external layer can be weak neutral by appropriate choice of the layer elastic constants. The effective field method is used for determination of the effective elastic stiffness tensor of a homogeneous isotropic medium containing a random set of radially transverse isotropic inclusions.

255 Anchor Talk: Consider intrinsic factors that regulate homeostasis to optimize sustainability of mineral supplements for swine

Abstract Decades of research has focused on methodologies to improve the efficiency of mineral use while assuring sufficient intake to meet animal well-being and production needs. A primary focus of these efforts is P, as P is the third most expensive category of nutrients supplemented in swine diets. Bioavailability of P is more variable than other nutrients in feed ingredients commonly fed to swine. Due to complexities involved in assessments of P bioavailability efforts shifted to defining P digestibilities for each ingredient. Efforts to refine P digestibilities, based on intake and fecal excretion, even with corrections for endogenous losses, have failed to provide a constant coefficient for feed ingredients that can be included in diet formulations, as the digestibility estimates vary with animal age, production phases and inclusion of enzymes such as phytase. An under-appreciated contribution to inaccuracies of digestible P relates to intrinsic regulation of Ca and P homeostasis by the animal. Regulation of Ca and P homeostasis by PTH and 1,25(OH)2D3, must now include a third mineralotropic hormone, FGF23. Applying insights for intrinsic roles of FGF23 will allow more efficient use of nutrients, especially P and vitamin D. FGF23 regulates activation of vitamin D and controls renal P excretion. Over-supplementation of P signals osteocytes (bone cells embedded in a mineralized matrix) to release intact FGF23 which targets the kidney to block reabsorption of P for maintenance of soft tissue homeostasis, resulting in an inefficient use of dietary P. Intact FGF23 also inhibits hydroxylation of 25-OH D3 to form 1,25(OH)2D3. These endocrine pathways illustrate major roles provided by kidneys and bone to allow adaptation to variable Ca and P inputs, thus maintaining homeostasis. Recent efforts to assess P requirements of sows during gestation and lactation illustrate the sensitivity of using renal excretion of Ca and P to assess requirements. Based on 24-h collections, urine Ca:P ratios > 1.5 were consistent with deficient P intake, ratios from 0.5 to 1.5 reflected P adequacy, and ratios < 0.5 indicated excessive P intake. As a practical method, spot urine samples collected at variable times throughout the day reliably predicted Ca:P ratios in 24-h urine collections. Thus, a simplified approach using Ca to P ratio in spot urine samples can be used to assess P intake adequacy. This practical approach can be applied in commercial sow herd to allow herd-based assessment of P status. In conclusion, within herd assessments, based on urine Ca:P ratios, can be used to determine if P supplements are deficient, adequate, and excessive. As such, significant progress can be made to provide a balance between the need to adequately meet animal need with efforts to minimize negative environmental impacts from over-supplementation of P.

A new dynamic Monte Carlo method satisfying n-particle diffusion equation with position-dependent diffusion coefficient, free energy, and intermolecular interactions.

A dynamic Monte Carlo (MC) method recently proposed by us [Nagai et al., J. Chem. Phys. 156, 154506 (2022)] to describe single-particle diffusion of a molecule in a heterogeneous space with position-dependent diffusion coefficient and free energy is generalized here to n-particle dynamics, where n molecules diffuse in heterogeneous media interacting via their intermolecular potential. Starting from the master equation, we give an algebraic proof that the dynamic MC transition probabilities proposed here produce particle trajectories that satisfy the n-particle diffusion equation with position-dependent diffusion coefficient D0i(ri), free energy F1i(ri), and intermolecular interactions Vij(ri, rj). The MC calculations based on this method are compared to molecular dynamics (MD) calculations for two-dimensional heterogeneous Lennard-Jones test systems, showing excellent agreement of the long-distance global diffusion coefficient between the two cases. Thus, the particle trajectories produced by the present MC transition probabilities satisfy the n-particle diffusion equation, and the diffusion equation well describes the long-distance trajectories produced by the MD calculations. The method is also an extension of the conventional equilibrium Metropolis MC calculation for homogeneous systems with a constant diffusion coefficient to the dynamics in heterogeneous systems with a position-dependent diffusion coefficient and potential. In the present method, interactions and dynamics of the real systems are coarse-grained such that the calculation cost is drastically reduced. This provides an approach for the investigation of particle dynamics in very complex and large systems, where the diffusing length is of sub-micrometer order and the diffusion time is of the order of milliseconds or more.

Convergence analysis of a decoupled pressure-correction SAV-FEM for the Cahn–Hilliard–Navier–Stokes model

In this paper, a linear, decoupled and unconditional energy-stable numerical scheme of Cahn–Hilliard–Navier–Stokes (CHNS) model is constructed and analyzed. We reformulate the CHNS model into an equivalent system based on the scalar auxiliary variable approach. The Euler implicit/explicit scheme is used for time discretization, that is, linear terms are implicitly processed, nonlinear terms are explicitly processed, and pressure-correction method of the Navier–Stokes equations is also adopted. In this way, we achieve the decoupling of phase field, velocity and pressure, and only need to solve a series of linear equations with constant coefficients at each time step, thereby improving computational efficiency. Then the finite element method is used for space discretization, and the finite element spaces of phase field, velocity and pressure are taken as Pl−Pl−Pl−1 respectively. We also verify that the proposed scheme satisfies the discrete energy dissipation law. The optimal error estimates of the fully discrete scheme is proved, which the phase field, velocity and pressure satisfy the first-order accuracy in time and the (ℓ+1,ℓ+1,ℓ)th order accuracy in space, respectively. Finally, numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.

Comprehensive Six-Degrees-of-Freedom Trajectory Design and Optimization of a Launch Vehicle with a Hybrid Last Stage Using the PSO Algorithm

Increased performance with reduced overall cost, and precise design and optimization of launch systems are critical to affordability. In this respect, the use of hybrid motors has increased to ease handling based on motor selection. In the current study, the launch vehicle’s performance is enhanced by incorporating a hybrid rocket motor into the last stage and optimized using particle swarm optimization to develop a six-degrees-of-freedom tool. This modification aims to increase payload placement flexibility, facilitate handling, and reduce costs. Thanks to the interactive subsystems within this research, this innovative study more comprehensively considers the launch vehicle trajectory design problem, allowing the simultaneous consideration of the effect of launch vehicle geometry along with other parameters in the system. In this context, the proposed method is applied to the Minotaur-I launch vehicle, and contributions of the detailed design and optimization are presented. Optimization results show that the percentage differences between these models for the original vehicle were observed to be 11.55% in velocity and 8.02% in altitude. However, there were differences of 10.06% and 48.8%, 15.8% and 23.2%, and 19.5% and 78.9% in altitudes and velocities when the center of gravity and moment of inertia changes were neglected, and constant aerodynamic coefficients were assumed, respectively. In all these cases, it was observed that the flight path angle was not close to zero. Moreover, the same mission was achieved by the launch vehicle with the optimized hybrid last stage and the propulsion performance was increased by about 7.64% based on the specific impulse and total impulse-over-weight ratio.

Experimental and Theoretical Investigation on the SR method grown Semi-Organic Piperazinium Tetrachlorozincate Monohydrate (PTZM) Single Crystal for Optoelectronic Applications

Efficient semi organic nonlinear optical (NLO) Piperazinium Tetrachlorozincate monohydrate (PTZM) [C4H12N2][ZnCL4].H2O single crystals have been grown by slow evaporation solution technique (SEST) and Sankaranarayanan-Ramasamy (SR) method using water as solvent. Single crystal X-ray diffraction (SXRD) analysis reveals the unit cell parameters of the grown crystal. The morphology of the grown crystal was identified by the single crystal XRD analysis. The electrical properties, dielectric constant, dielectric loss and piezoelectric (d33) coefficient were determined. The etch pit density of PTZM crystal has been calculated by using the chemical etching analysis. The laser damage threshold (LDT) analysis was investigated by Nd: YAG laser and the wavelength of laser is 1064nm. The mechanical stability of the grown PTZM crystal was studied using Vickers microhardness measurement. Utilizing quantum chemical calculations, the PTZM compound is analyzed for vibrational properties, HOMO and LUMO characteristics, NBO interactions, and the determination of first-order hyperpolarizability. The nonlinear susceptibility and first-order hyperpolarizability results provide compelling evidence and affirm the PTZM molecule’s potential as a strong candidate for nonlinear optical (NLO) applications.

Stationary trajectories in Minkowski spacetimes

We determine the conjugacy classes of the Poincaré group ISO+(n, 1) and apply this to classify the stationary trajectories of Minkowski spacetimes in terms of timelike Killing vectors. Stationary trajectories are the orbits of timelike Killing vectors and, equivalently, the solutions to Frenet–Serret equations with constant curvature coefficients. We extend the 3 + 1 Minkowski spacetime Frenet–Serret equations due to Letaw to Minkowski spacetimes of arbitrary dimension. We present the explicit families of stationary trajectories in 4 + 1 Minkowski spacetime.

Results of the analytical solution of the problem of radial vibrations of disks of variable thickness

An analytical solution is obtained for the problem of radial vibrations of disks of variable thickness. A disk is considered that is rigidly fixed along the inner circular contour (ρ=0.2) and free on the outer contour (ρ=1). The thickness of the disk varies according to the law H=H0(ρν+μ+Cρν-μ)2, where H0,C,μ are arbitrary constants; ν is the Poisson's ratio. The exact solution of the problem is known only for H=const and H=1/ρ3. However, these solutions are not sufficient to study the vibrations of disks of other configurations. The proposed law of thickness variation H(ρ) allows us to obtain exact solutions to the problem at any value of the constant coefficients H0, C, μ, ν. By varying the values of these coefficients within a single given function, it is possible to set the disk profile of the desired appearance. The methods used to obtain these solutions are based on appropriate mathematical transformations of the original equation. The problem of disk oscillations is solved for four variants of thickness change. The natural frequencies for the first three forms of vibration are calculated. Comparison of the natural frequencies found for the three cases of the disk profile gently sloping indicates an increase in their values with an increase in the bending of the disk thickness. Based on the obtained eigenfunctions, the stresses were calculated and the nature of their distribution along the radial coordinate of the disk was determined. The strength of the disks under resonant radial vibrations was evaluated using a special criterion. It is found that the most limiting, i.e., destructive principal stress σ1=σr at the first (main) form of vibration should be chosen from the ratio σr≈0.79 [σ-1], where [σ-1] is the endurance limit of the disk material under uniform loading. The results obtained can be used to predict the stress-strain state of disks of variable profile under their radial vibrations

A general fourth-order mesoscopic multiple-relaxation-time lattice Boltzmann model and its macroscopic finite-difference scheme for two-dimensional diffusion equations

In this work, we first develop a general mesoscopic multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the two-dimensional diffusion equation with the constant diffusion coefficient and source term, where the D2Q5 (five discrete velocities in two-dimensional space) lattice structure is considered. Then we exactly derive the corresponding macroscopic finite-difference scheme of the MRT-LB model. Additionally, we also propose a proper MRT-LB model for the diffusion equation with a linear source term, and obtain a macroscopic six-level finite-difference scheme. After that, we conduct the accuracy and stability analysis on the finite-difference scheme and the mesoscopic MRT-LB model, and find that at the diffusive scaling, both of them can achieve a fourth-order accuracy in space based on the Taylor expansion. The stability analysis also shows that they are both unconditionally stable. Finally, some numerical experiments are conducted, and the numerical results are also consistent with our theoretical analysis.

Effect of Deposition Pressure and Temperature on Tungsten Thin-Film Heater for Phase-Change Switch Applications

Tungsten (W) film is increasingly utilized in various microheater applications due to its numerous advantages. These advantages include a high melting point, positive constant temperature coefficient of resistance (TCR), good mechanical stability, and compatibility with semiconductor processes. In this paper, deposition parameters for enhancing the properties of W film were investigated, and an optimized microheater was fabricated. It was found that the deposition temperature and pressure can modify the TCR to be negative or positive and the crystalline phase of W films to be alpha phases or mixed with beta phases. A W film deposited under 650 °C with a pressure of 1 pa has a positive TCR and pure alpha phase crystalline structure. We applied this optimized W film as a microheater in an RF phase-change switch (RFPCS), and the maximum voltage of the optimized W microheater increased by at least 48% in this work. By optimizing the microheater, the phase-change switch can be successfully actuated in both on and off states, demonstrated by the Raman results of the phase-change material. A voltage pulse of 20 V/200 ns was enough to turn the switch off with MΩ, and 11 V/3 μs could turn the switch on with 138 Ω. The optimized microheater and device can cycle 500 times without failure. The insertion loss and isolation of the device at 20 GHz was 1.0 dB and 22 dB.

Hexagonal finite differences for the two-dimensional variable coefficient Poisson equation

For many years, finite differences in hexagonal grids have been developed to solve elliptic problems such as the Poisson and Helmholtz equations. However, these schemes are limited to constant coefficients, which reduces their usefulness in many applications. The main challenge is accurately approximating the diffusive term. This paper presents examples of both successful and unsuccessful attempts to obtain accurate finite differences based on a hexagonal stencil with equilateral triangles to approximate two-dimensional Poisson equations. Local truncation error analysis reveals that a second-order scheme can be achieved if the derivative of the diffusive coefficient is included. Finally, we provide numerical examples to verify the accuracy of the proposed methods.

Analyzing Lower Limb Dynamics in Human Gait Using Average Value-Based Technique

The motivation of this study is to develop effective and economical assistive technologies for people with physical disabilities. The novelty in this manuscript is the application of the average value-based technique to accurately represent the involved biomechanics of the lower limb joints during the human gait cycle. This mathematical formulation of lower limb joints’ biomechanics forms the first objective for modeling and final exoskeleton prototype development. To account for modeling the characteristics of human locomotion, the nth-order linear differential equation with constant coefficients is considered with appropriate modification. The physical characteristics of an individual are represented by the constant coefficients (P0, P1, P2, and P3) of the modified infinite series, which are obtained by processing experimental data collected using an optical technique. The differential terms of the infinite series are replaced by difference terms (δbavg, δ2bavg, and δ3bavg) since the data were captured as a set of digital values. The work presented here is based on the experimental results of individuals suitably categorized according to their physical nature like age and other physical structure. The optically monitored positional values of the lower limb joints of the individual subjects while they are completing the gait cycles are used for getting values of different terms of the model. The data collected through the conduct of experiments are used for finding the values of the terms of the differential equation. The model is effectively validated through experimental results. It was determined that the representation’s accuracy fell within the ±5% acceptable tolerance limit. The model is prepared for healthy as well as disabled persons, through which the disability is quantified. The resulting model can be used to develop assistive devices for people with physical disabilities. This results in the rehabilitation process and thereby helps the reintegration into society, subsequently allowing them to lead a normal life.

Adaptive neural event‐triggered near‐optimal control for affined uncertain nonlinear discrete‐time system

AbstractA novel event‐triggered heuristic dynamic programming (HDP) algorithm is proposed for the near‐optimal control of uncertain discrete‐time nonlinear input‐affine systems. Based on input‐to‐state stability (ISS) analysis, a new event‐triggered mechanism (ETM) is designed. Under constant coefficients, a Lipschitz‐like assumption that forms the basis of the event‐triggering condition is considered to be conservative. To further reduce the conservativeness of the triggering condition and enlarge the average interevent time, an adaptive threshold parameter is utilized in the proposed ETM. In the HDP algorithm framework, model, critic, and action network are adopted to achieve state estimation, approximation to the optimal cost function, and solution to Hamilton–Jacobian–Bellman (HJB) equation. Under the proposed event‐triggered HDP algorithm, the closed system is proved to possess semiglobal uniform ultimate boundedness (SGUUB). Finally, by conducting simulation, it shows that on the premise of satisfying control performance, the event‐triggered strategy can realize reduction on the updating frequency of the controller.

The Dynamical Equations of the Restricted Three-Body Problem with Poynting-Robertson Drag Force and Variable Masses

The restricted three-body problem (R3BP) is a formulation which defines the motion of a passively gravitating test particle having  infinitesimal mass and moving in the gravitational environment of two bodies, called primaries. The R3BP is still an exciting and active  research field that has been getting attention of scientists and astronomers because of its applications in dynamics of the solar and stellar systems, lunar theory, and artificial satellites. The equations of motion are usually the starting point in the investigations of the  dynamical predictions of the infinitesimal mass. Therefore, in this paper, we examine the derivations of the dynamical equations of the  R3BP with Poynting-Robertson (P-R) Drag force and variable masses. In this model formulation, both primaries are assumed to vary their  masses under the combined Mestschersky law (CML) and they move in the frame of the GyldenMestschersky equation (GME). Further,  the bigger primary is assumed to be emitting radiation force, which is a component of the radiation pressure and the P-R drag. The non- autonomous dynamical equations of the model are derived and converted into the autonomized equations with constant coefficients  using the Mestschersky transformation (MT), the CML, the particular solutions of the GMP, and a transformation for the time dependent  velocity of light. We observed that the P-R drag of the bigger primary depends on the mass parameter, radiation pressure, velocity of  light and the mass variation constant . The derived systems of equations with variable and constant coefficients can be used to model  the long-term motion of satellites and planets in binary systems.